Video: Writing and Evaluating Numerical Expressions in a Real-World Context

To change a temperature given in degrees Celsius to degrees Fahrenheit, first multiply the Celsius temperature by 9, then divide the answer by 5, and then add 32 to the result. Given the shown table, determine the difference between the average monthly temperatures of January and June after converting them to degrees Fahrenheit.

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Video Transcript

To change a temperature given in degrees Celsius to degrees Fahrenheit, first, multiply the Celsius temperature by nine, then divide the answer by five, and then add 32 to the result. Given the shown table, determine the difference between the average monthly temperatures of January and June after converting them to degrees Fahrenheit.

Our table gives us the average monthly temperature for three months in degrees Celsius. But we’re interested in the difference in degrees Fahrenheit, which means our first step will be converting these degrees Celsius temperatures into Fahrenheit. And we’ve been given the steps we need to do that. Since we’re interested in the difference between January and June, these are the two months we’ll focus on converting. First, we multiply the Celsius temperature by nine. For January, that’s seven times nine. And for June, that’s 22 times nine. Whatever that result is, we then divide by five. That would be seven times nine divided by five and 22 times nine divided by five.

And our last step is to add 32 to the result. So we’ll have seven times nine divided by five plus 32 and 22 times nine divided by five plus 32. Let’s, first, consider the January temperature. First, we have seven times nine, which equals 63. We can bring everything else down. And then we’ll need to divide 63 by five. To do that, we say that five can go into six one time with a remainder of one. And five can go into 13 two times with a remainder of three. And that means we’ll need to add a decimal and a zero. From there, we’ll ask, how many times does five go into 30? That’s six times and we bring up the decimal. Since six times five is 30, there’s no remainders. And we say that 63 divided by five is 12.6. We need to bring down the plus 32. 12.6 plus 32 equals 44.6. And so we can say that the average temperature in January in degrees Fahrenheit is 44.6 degrees Fahrenheit.

Now, we’ll follow the same procedure for June. We need to multiply 22 by nine. We know that 20 times nine is 180 and two times nine equals 18. And so we can say that 22 times nine equals 198. Then we bring everything else down and we have 198 divided by five plus 32. So we’ll need to divide 198 by five. We can use the same process. Five goes into 19 three times. Three times five is 15. So there is a remainder of four. Then we say, how many times does five go into 48? That is, nine times; nine times five is 45. This means we have a remainder of three and we’ll need to add a decimal and a zero.

From there we’ll ask, how many times does five go into 30? Six times and we bring up the decimal. 198 divided by five equals 39.6. And so we add 32. This equals 71.6. And we can say that the average monthly temperature in degrees Fahrenheit in June is 71.6 degrees Fahrenheit. Now that we know the average monthly temperatures in Fahrenheit for January and June, we’re ready to find the difference. To do that, we take 71.6 and we subtract 44.6 and we get 27.0. And so we can say that the difference between the average monthly temperature of January and June after converting them to degrees Fahrenheit would be 27 degrees Fahrenheit.

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